A274461 Least common multiple of first n proper prime powers.

1, 4, 8, 72, 144, 3600, 10800, 21600, 1058400, 2116800, 6350400, 768398400, 3841992000, 7683984000, 1298593296000, 3895779888000, 7791559776000, 2251760775264000, 15762325426848000, 5690199479092128000, 11380398958184256000, 6020231048879471424000, 30101155244397357120000, 90303465733192071360000

Offset

0,2

Comments

Squares in this sequence include a(0)=1^2, a(1)=2^2, a(4)=12^2, a(5)=60^2, a(10)=2520^2, and a(11)=27720^2. Are there any more?

All terms in this sequence are powerful numbers (A001694).

Links

Table of n, a(n) for n=0..23.

Mathematica

t = Join[{1}, Select[Range@ 1000, Min@ FactorInteger[#][[All, 2]] > 1 &]]; Union@ Table[LCM @@ t[[1 ;; n]], {n, 45}] (* Michael De Vlieger, Jun 24 2016, after Harvey P. Dale at A001694 *)

Prog

(PARI) alist(n)=my(pp=0, x=1); vector(n, k, while(isprimepower(pp++)<2&&pp!=1, 0); x=lcm(x, pp))

Crossrefs

Cf. A051451, A246547, A001694.

Sequence in context: A228930 A051226 A013112 * A240503 A383344 A221484

Adjacent sequences: A274458 A274459 A274460 * A274462 A274463 A274464

Keyword

nonn

Author

Franklin T. Adams-Watters, Jun 23 2016

Status

approved